Related papers: Large Deviations for Stochastic Differential Equat…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
We establish a large deviation principle (LDP) for a class of stochastic porous media equations driven by L\'{e}vy-type noise on a $\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, with the Laplacian replaced by a negative definite…
The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…
We prove the small-noise large deviation principle (LDP) for stochastic evolution equations in an $L^2$-setting. As the coefficients are allowed to be non-coercive, our framework encompasses a much broader scope than variational settings.…
We investigate the large deviation principle (LDP) of the stationary solutions of stochastic functional differential equations (SFDEs) with infinite delay under small random perturbation. First, we demonstrate the existence and uniqueness…
We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two…
Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into variational principles through the concept of a semi-martingale driven variational…
We shall consider a stochastic maximum principle of optimal control for a control problem associated with a stochastic partial differential equations of the following type: d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt +…
We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly.…
In this paper, we establish the large deviation principles for stochastic porous media equations driven by time-dependent multiplicative noise on $\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, and the Laplacian replaced by a…
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of…
It is well known that symplectic methods have been rigorously shown to be superior to non-symplectic ones especially in long-time computation, when applied to deterministic Hamiltonian systems. In this paper, we attempt to study the…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.
We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.
In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…
In this paper, we establish a large deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. The weak convergence method introduced by Budhiraja, Dupuis and Maroulas in [5] plays a key role.
The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
In this article we establish a large deviation principle for the family {\nu_{\epsilon}:\epsilon \in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrt{\epsilon}}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…