We consider Backward Stochastic Differential Equations (BSDEs) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition and the generator to depend on a vector parameter x. We give sufficient conditions for the solution pair of the BSDE to be differentiable in x. These results can be applied to systems of forward-bac...

A receding horizon filtering problem for nonlinear continuous-time stochastic systems is considered. The paper presents the optimal receding horizon filtering equations. Derivation of the equations is based on the Kushner-Stratonovich and Fokker-Planck-Kolmogorov equations for conditional and unconditional density functions. This result could be a theoretical basis for the optimal control in no...

We prove that the stationary distribution of a system of reacting species with a weaklyreversible reaction network of zero deficiency in the sense of Feinberg admits tensor-structured approximation of complexity which scales linearly with respect to the number of species and logarithmically in the maximum copy numbers as well as in the desired accuracy. Our results cover the classical mass-acti...

Abstract. A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y (t)) on (T × {1, 2} × R), where T is the twodimensional torus. Here (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance. Y (t) is an additive functional of K, define...

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. Under regularity assumptions, we use results from standard risk-sensitive differential game theory to show that the mean-field value of the exponentiated cost functional coincides with the value function of a Hamilton-Jacobi-Bellman-Fleming (HJBF) equation with an additional quadratic term. We provide an...

A summary of the relationship between the Langevin equation, Fokker-PlanckKolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of the path integral formula is demonstrated via some nontrivial examples. Specifically, it is shown...

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y...