In this paper, the concepts of conditional m -spacings are introduced when a series system with independent and identically distributed (i.i.d.) components fails at a given time t . First, we prove that the conditional spacings Di,n-11,t preserves the log-convexity of the parent density, while the conditional m -spacings Di,n-1m,t(m >= 2) preserve its log-concavity. Second, we extend the likelihood ratio order and hazard rate order from m -spacings to conditional m -spacings. In addition, we present some examples involving Pareto and Gamma distributions.
COVID-19 is a global pandemic that has significantly impacted societies and healthcare systems worldwide. Therefore, understanding its complex effects requires thorough analysis. This study focused on the second wave of COVID-19 in India and Brazil, utilizing a compartmental model that incorporated the Beddington-DeAngelis incidence and Holling Type-II treatment functions to better understand transmission dynamics and the effects of medical interventions. Data fitting was conducted using Python, while simulations and all other analyses, including sensitivity analysis to explore implications for disease control strategies, were performed using MATLAB. The study also extended the model to a stochastic framework by incorporating white noise, allowing a comparison between the deterministic and stochastic approaches. The deterministic model provided a baseline understanding of the transmission dynamics and stability, while the stochastic model captured potential variability in outcomes, including disease extinction and stochastic permanence.
The Chilean State provides resources to the Universities of the Rectors' Council of Chile to finance their management through a competitive allocation model called the Direct Government Subsidy (AFD). This study analyzes whether the subsidy promotes efficient and productive management, given the specificity of the model. The distribution initiated in 1981 is compared with the assigned contributions for 2020, revealing that AFD is not related to higher academic productivity but responds to targeting in the definition of administration variables, without necessarily increasing academic productivity. The AFD public policy needs revision to incentivize and reward productivity while preventing negative side effects. Path Analysis (a special case of Structural Equation Models - SEM) and the Partial Least Squares - PLS approach are used to justify the relationships.
This paper contains the description of the odd fractional Brownian motion (ofBm), that is a centered Gaussian process arising as the "odd" combination of the values of fractional Brownian motion defined on the whole R. The analysis carried out shows that, unlike the standard fBm, ofBm exhibits non-stationary increments, while demonstrating shortterm or long-term dependence, in the same ranges of Hurst index values as a fractional Brownian motion. It is proved that ofBm has a property of locally nondeterminism, a key result that allows to demonstrate the existence of a jointly continuous local time. Also, it is proved that central limit theorem for functionals of two independent ofBms is true. These results, in particular, provide the possibility to use ofBm as a tool for modeling non-stationary processes with long-and short-range memory.
This paper studies two-parameter stochastic differential inclusions involving mixed-type stochastic integrals. For such inclusions, we establish a Filippov-type theorem in the stochastic setting, ensuring the existence of solutions and providing quantitative estimates comparing quasi-solutions with the solution set. As an application of the main result, we examine continuity properties of the solution sets as well as the attainable sets with respect to the right-hand side of the inclusion.
Infinite activity L & eacute;vy processes with no Brownian motion component are considered. The sum of the compensated small jumps is approximated by a suitably scaled Brownian motion according to Asmussen and Rosinski (2001). To compute the sensitivity measure Delta for a European type option price, integration by parts is applied to both the approximating Brownian motion following the Malliavin integration by parts approach on the Wiener space as in for instance Fourni & eacute; et al., where there are no jumps, and the integration by parts with respect to the remaining jumps following Bavouzet-Morel and Bally et al., with a reasonable weighting of the two types of integration by parts, here depending on the maximum size of the approximated compensated jumps. The weighted integration by parts is shown to hold under suitable moment conditions valid also for non-differentiable payoff functions. Optimal weights in a class of weights depending on the maximum size of the approximated compensated jump sizes is investigated analytically and numerically. Furthermore, convergence rate for the pay-off of the small-jump approximation, known for European puts, is established also for European calls. The mean number of needed simulated jumps for a given tolerance level is also accounted for.
In this paper, the existence of solutions and the stability results are derived for impulsive Hilfer fractional integrodifferential stochastic systems (IDSSs) with Poisson jumps in Rn space. The main results are obtained by using fractional calculus, stochastic analysis approach, and measure of non-compactness (MNC) via M o & uml; nch fixed point technique for the first time in the literature to the finite dimensional space. For the stability result, boundedness properties of Mittag-Leffler (M-L) function is effectively used. Two numerical examples are given for verification of theoretical results.
This paper first presents a new definition of pseudo almost automorphic stochastic processes in distribution, and then applies inequality techniques and Banach fixed point theorem to establish the existence and global exponential stability of pseudo almost automorphic solutions in distribution for a class of mean field stochastic differential equations driven by Brownian and fractional Brownian motions. The results and methods presented in this paper are both novel.
Diffusion processes for modeling, among other fields, (macro-) econometrics, mathematical finance, biology, queueing, and electrical engineering often involve reflection at one or two barriers in order to restrict the state space of the process, which returns continuously and immediately to the interior of the state space when it attains a one-sided barrier. In this paper, we investigate the L2 structure and estimation of such processes. The methodology of estimation is built upon the least squares (LS) approach for one-dimensional continuous-time ergodic reflected bilinear (RCOBL) processes. Our estimation procedure is based on continuously and/or discretely observed processes. So, We provide expressions for the moments up to the n-th order and derive explicit formulas for the parameter estimates involved in the process. Additionally, we establish the strong consistency and asymptotic normality (CAN) of the parameters estimates. Numerical results and empirical analysis are proposed to illustrate our theory.
This work focuses on multiscale multivalued McKean-Vlasov stochastic systems. First, we employ the contractive mapping principle to establish the well-posedness of fully coupled multivalued McKean-Vlasov stochastic systems under non-Lipschitz conditions. Subsequently, for multiscale multivalued McKean-Vlasov stochastic systems perturbed by small noises, we prove a large deviation principle using a weak convergence method. As a by-product, two averaging principles are also derived.
This work aims to investigate the nonlinear time-fractional impulsive Navier-Stokes equation in Hilbert space driven by fractional Brownian motion. To start with, the non-linear stochastic partial differential equation is remodeled by using the Helmholtz-Hodge projection operator, stochastic calculus, and the Stokes operator. The existence of mild solution is obtained through the application of Mittag-Leffler functions, Krasnoselskii's fixed point theorem, and stochastic analysis. The approximate controllability result is obtained for the presented system under suitable assumptions. Finally, a suitable application for turbulence control, which is an aircraft model in automobile engineering is presented and validated the obtained theoretical results.
In this article, we analyze a class of Hamiltonian systems whose phase portrait consists of Gaussian curves. The class of Hamiltonian systems is unstable because the trajectories approach infinity along the x-axis. We consider perturbing the systems in two distinct ways: (1) a small deterministic push toward the origin that preserves the qualitative behavior of the systems and (2) constant white noise. We prove that neither perturbation by itself is sufficient to stabilize the class of Hamiltonian systems, but that the combination of both perturbation types results in stabilization by creating quasi-periodic behavior.
In this article, we consider the asymptotical behavior of solutions of the non-autonomous reaction-diffusion equations with polynomial growth nonlinearity of arbitrary order and dynamic boundary conditions driven by nonlinear colored noise. We first prove the existence of weak solutions by the Faedo-Galerkin methods, but the uniqueness of solutions cannot be guaranteed due to the lack of Lipschitz continuity of diffusion and nonlinear terms. Then we establish the asymptotical compactness of the corresponding cocycle by the Sobolev compactness embedding theorem and the measurability of the random attractor by proving the weak upper semi-continuity of the multi-valued non-autonomous cocycle. Finally, we prove the existence and uniqueness of a pullback random attractor for the associated multi-valued non-autonomous cocycle.
Recent regulatory overhauls in North America and Europe require insurers the detailed revision of capital requirements across multiple insurance product domains. These cover unique challenges akin to guaranteed minimum benefits in variable annuities and risk correlations. This article addresses the urgent need to establish robust pricing methodologies for option-embedded guarantees. Our focus is on the pricing of a guaranteed annuity option (GAO), which offers investors with both growth prospects and downside protection. We propose a stochastic correlation framework to capture the dynamic dependence between financial and longevity risks. When the traditional Monte-Carlo method is used as a baseline, our change of probability measures approach not only generates accurate GAO values but also features a remarkably efficient computation. An analysis of the magnitude and direction of the impact of the model parameters on GAO prices is also presented. Both the theoretical and applied contributions of this article have central importance to insurers and regulators alike and to the concerted efforts in sustaining the insurance sector's stability and consumer protection.
In [5] a family of processes that converge strongly toward Brownian motion, defined from renewal processes, are constructed. In this paper we prove that some of these processes can be utilized to build approximations of Gaussian processes such as fractional Brownian motion or multiple Stratonovich integrals and we provide sufficient conditions on renewal processes to ensure that the convergence holds. An illustrative example of such a Gaussian process is the fractional Brownian motion with any Hurst parameter.
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider both stochastic calculus and white noise filtering methods and derive measure-valued evolution equations for the nonlinear filter and prove existence and uniqueness theorems for the solutions. We will also study first order approximations to these measure-valued evolutions by linearizing the wave equations and characterize the filter dynamics in terms of infinite dimensional operator Riccati equations and establish solvability theorems.
In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to the solution of partial or ordinary differential equation. As such, there are two primary difficulties in maximizing the marginal likelihood (i) that the solution of differential equation is not always analytically tractable and (ii) neither is the marginal likelihood. Typically (i) is dealt with using a numerical solution of the differential equation, leading to a numerical bias and (ii) has been well studied in the literature using, for instance, Markovian stochastic approximation. It is well-known that to reduce the computational effort to obtain the maximal value of the parameter, one can use a hierarchy of solutions of the differential equation and combine with stochastic gradient methods. Several approaches do exactly this. In this paper we consider the asymptotic variance in the central limit theorem, associated to known estimates and find bounds on the asymptotic variance in terms of the precision of the solution of the differential equation. The significance of these bounds are the that they provide missing theoretical guidelines on how to set simulation parameters; that is, these appear to be the first mathematical results which help to run the methods efficiently in practice.
We develop a quantitative contraction framework for Schr & ouml;dinger and Sinkhorn bridges based on transportation-cost inequalities and Riccati matrix difference equations. Our approach combines logarithmic Sobolev and Talagrand-type inequalities to obtain explicit entropy and Wasserstein contraction bounds for Sinkhorn bridge measures, entropic optimal transport plans, and the associated Markov transport maps. A key feature of the analysis is the interplay between transport-cost inequalities and matrix Riccati difference equations arising in filtering and stochastic control. The results are established under local regularity assumptions on the reference transition, formulated in terms of curvature, Lipschitz continuity, and Fisher-information bounds. Within this general setting, we derive quantitative stability and convergence estimates for Schr & ouml;dinger bridges and Sinkhorn iterates that are robust with respect to the choice of reference measure. As a main application, we specialize the theory to linear-Gaussian reference transitions, where the Gaussian structure permits sharp constants, refined exponential decay rates, and continuity estimates for Schr & ouml;dinger bridges, Sinkhorn iterates, barycentric projections, conditional covariances, and proximal sampler semigroups. In this setting, we recover and extend several known contraction results for entropic and Wasserstein distances and obtain new quantitative bounds that improve previously available rates. Our results provide a unified probabilistic framework for stability, regularity, and convergence of Sinkhorn algorithms. We illustrate the impact of our results on regularized entropic transport, proximal samplers, and diffusion-based generative models, as well as on diffusion flow-matching.
