In this paper, under non-Lipschitz condition, we shall prove the homeomorphic flow property of solution to multidimensional stochastic differential equation (SDE) driven simultaneously by fractional Brownian motion with H is an element of ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} and standard Brownian motion.
In this paper, we establish the existence and uniqueness of a solution for multidimensional generalized backward stochastic differential equations where the noise is driven by a Brownian motion and an independent Poisson random measure. We consider the case where the generators are weakly monotone and satisfy a general growth condition. Our results are derived using a priori estimates, the convolution approach and truncation techniques
Employing an iterative method, we establish the existence and uniqueness solution of psi-Riemann-Liouville fractional stochastic differential equations. Examples are provided to illustrate our results.
We investigate generalized backward stochastic differential equations with two reflecting barriers. Under the conditions that the barriers are completely separated and the generators are monotone, we establish a general result regarding the existence and uniqueness of the solution. In the Markovian framework, this result is applied to prove the existence and uniqueness of the viscosity solution to an obstacle problem for a partial differential equation with nonlinear Neumann boundary conditions.
In this paper, we investigate a class of Riemann-Liouville-type fractional stochastic functional differential equations driven by L & eacute;vy noise. By using It & ocirc; formula for the considered equation and using the Lyapunov technique, some sufficient conditions ensuring that the solutions of the considered equations are h-stable in p-th moment sense are obtained. Furthermore, by using a novel approach, some new and exhibit criteria for the h-stability for the considered equations are obtained. Finally, two examples are provided to illustrate the effectiveness of our main results.
The consistency of the estimators G 55 {G_{55}} and G 59 {G_{59}} for quadratic forms of the regularized inverse covariance matrix is proven.
In this work, we study the existence and uniqueness of mild solution for a mean-field stochastic integrodifferential equation (SIDEs) with finite delay, driven by a fractional Brownian motion in a Hilbert space with Hurst parameter H > 1/2. We suppose that the linear part has a resolvent operator in the sense given in [R. C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273 1982, 1, 333-349]. An example is provided to show the applicability of our results.
This paper studies a risk-sensitive control problem on a finite time horizon with execution delays where the reward and intervention cost functions can belong to a large class of stochastic processes. In particular, the intervention cost function is modeled by right-continuous and left-limited processes that are quasi-left continuous. A probabilistic approach is adopted in this setting based on the Snell envelope concept. We characterize recursively optimal solutions to risk-sensitive control problems by recasting the control problem as an iterative optimal stopping problem. We show the existence of an optimal strategy and establish the connection between the approximation scheme and the associated total expected reward.
This paper aims to investigate the existence of & varepsilon;-optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by different external forces, which are feedback controls. To reach our objective, we use the finite-dimensional method. Furthermore, to illustrate the applicability of the result, we give some examples.
We introduce a new type of reflected backward stochastic differential equations (BSDEs) driven by optional semimartingale process with lower optional barrier and so-called regulated trajectories for which the reflection constraint is imposed on its main solution component, denoted as Y by convention, but in terms of its conditional expectation E [ Y t | & Gscr; t ] {\mathbb{E}[Y_{t}|\mathcal{G}_{t}]} on a general sub-filtration { & Gscr; t } {\{\mathcal{G}_{t}\}} . This paper is devoted to the question of existence and uniqueness of strong solutions of the conditional RBSDE under Lipschitz conditions and by combining the Snell envelope method with Skorokhod lemma. Thus the connection between optimal stopping problems and linear conditional RBSDEs is given. Moreover, an example of applications to mathematical finance is presented.
This paper addresses delay and anticipated backward doubly stochastic differential equations driven by fractional Brownian motion (fractional delay and anticipated BDSDEs) with Hurst parameter H is an element of ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} . In these equations, the generator at time t can depend not only on the past and present but also on future solutions. We establish the existence and uniqueness of solutions in the cases of both Lipschitz and integral-Lipschitz coefficients. The stochastic integral used throughout the paper is of the divergence type.
In this paper, by investigating Nemytskij operators of random operators, we give out some common random fixed point theorems for measurable random operators. Some random fixed point theorems for probabilistic contractions are also presented. Noting that the random operators are assumed to be measurable instead of being continuous.
The consistency of the estimator G 55 {G_{55}} for quadratic forms of the regularized inverse covariance matrix is proven.
In this paper, we are concerned with an optimal control problem where the system is driven by a G-stochastic differential equation. Using the associated adjoint equation, where an admissible set of controls is convex, we establish necessary as well as sufficient optimality conditions for relaxed controls.
The paper presents the dynamical analysis of an avian influenza infection model in birds population with half-saturated incidence. The positivity of solutions is proved by the occurrence of a global positive solution. Also, we analyze the extinction scenario of infection under certain parametric restriction. Moreover, we define the reproduction ratio R 0 S R_{0}<^>{S} to examine the stochastic stability through the stationary distribution. In order to figure out when infection appears in the birds population and when it stops the spread, we derive the condition on R 0 S R_{0}<^>{S} . Furthermore, we generate some graphical simulations to support the theoretical results based on the value of reproduction ratio.
In this paper, we study the existence and the uniqueness of optional solutions of stochastic differential equations with respect to optional semimartingales by using a successive approximation method under a non-Lipschitz condition. The stability of solutions to non-Lipschitz SDEs is also considered, and the stochastic stability is obtained in the sense of mean square.
In this paper, we investigate doubly reflected generalized backward stochastic differential equations with two reflecting right-continuous with left-limited barriers in a general filtration supporting a Brownian motion and an independent integer-valued random measure. We establish the existence and uniqueness of the solution when the barriers and their left limits are completely separated without assuming Mokobodski’s hypothesis or the regularity condition.
This work addresses a switching control problem under which the cost associated with the changes of regimes is allowed to have discontinuities in time. Our main contribution is to show several characterizations of the optimal cost function as well as of epsilon-optimal control policies. This paper is an extension of [S. Hamad & egrave;ne, H. Jasso-Fuentes and Y. A. Osorio-Agudelo, On a switching control problem with c & agrave;dl & agrave;g costs, Stochastics 94 (2022), 1, 51-85] in the case of l & agrave;dl & agrave;g processes.
In this paper, we introduce the notion of quasi-(m, n)-paranormal operators on a Hilbert space and prove basic structural properties for the same class of operators. We also characterize these operators. We prove that if T is quasi-(m, n)-paranormal, then the spectral mapping theorem holds, that is, f(w(T)) = w(f(T)) for every analytic function f is an element of H(sigma(T)). We also show more general results for operators in the class.
In this paper, we introduce the notion of quasi- ( m , n ) (m,n) -paranormal operators on a Hilbert space and prove basic structural properties for the same class of operators. We also characterize these operators. We prove that if 𝑇 is quasi- ( m , n ) (m,n) -paranormal, then the spectral mapping theorem holds, that is, f ( w ( T ) ) = w ( f ( T ) ) f(w(T))=w(f(T)) for every analytic function f ∈ H ( σ ( T ) ) f\in\mathcal{H}(\sigma(T)) . We also show more general results for operators in the class.
