1,720,983 research outputs found
Dissipative backward stochastic differential equations in infinite dimensions
No full textWe prove an existence and uniqueness result for a class of backward stochastic dierential
equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of
stochastic partial dierential equations which can be solved with our result
L^p solution of backward stochastic differential equations driven by a marked point process
No full textWe obtain existence and uniqueness in L^p, p>1 of the solutions of a backward stochastic differential equations (BSDEs
for short) driven by a marked point process, on a bounded interval.
We show that the solution of the BSDE can be approximated by a finite system of deterministic differential equations.
As application we address an optimal control problems for point processes of general non-Markovian type and show that BSDEs can be used to prove existence of an optimal control and to represent the value function
Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity
No full textIn this paper we study a class of backward stochastic differential equations (BSDEs) of the form
dY_t = −AY_t dt − f_0(t, Y_t )dt − f_1(t, Y_t , Z_t )dt + Z_t dW_t , 0≤ t ≤ T ; Y_T = ξ
in an infinite dimensional Hilbert space H, where the unbounded operator A is sectorial and dissipative and
the nonlinearity f_0(t, y) is dissipative and defined for y only taking values in a subspace of H. A typical
example is provided by the so-called polynomial nonlinearities. Applications are given to stochastic partial
differential equations and spin systems
Optimal control for stochastic heat equation with memory.
Full text linkIn this paper, we investigate the existence and uniqueness of solutions for a class of evolutionary integral equations perturbed by a noise arising in the theory of heat conduction. As a motivation of our results, we study an optimal control problem when the control enters the system together with the noise
On the compensator of step processes in progressively enlarged filtrations and related control problems
Full text linkFor a step process X with respect to its natural filtration F, we denote by G the smallest rightcontinuous
filtration containing F and such that another step process H is adapted. We investigate
some structural properties of the step process X in G. We show that Z = (X,H) possesses the
weak representation property with respect to G. Moreover, in the case H = 1[τ,+∞), where τ is a
random time (but not an F-stopping time) satisfying Jacod’s absolute continuity hypothesis, we
compute the G-predictable compensator νG,X of the jump measure of X. Thanks to our theoretical
results on νG,X , we can consider stochastic control problems related to model uncertainty on the
intensity measure of X, also in presence of an external risk source modeled by the random time τ
Feedback optimal control for stochastic Volterra equations with completely monotone kernels.
Full text linkIn this paper we are concerned with a class of stochastic Volterra integro-dierential problems with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods. The application to optimal control provide other interesting result and require a precise descriprion of the properties of the generated semigroup. The rst main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The main technical point consists in the dierentiability of the BSDE associated with the reformulated equation with respect to its initial datum x
Filtering of continuous-time Markov chains with noise-free observation and applications
No full textLet X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set and let Y be defined by Y_t = h(X_t ), (t ≥ 0). We address the filtering problem for X in terms of the observation Y, which is not directly affected by noise. We write down explicit equations for the filtering process. We show that it is a Markov process with the Feller property. We also prove that it is a piecewise-deterministic Markov process in the sense of Davis, and we identify its characteristics explicitly. We finally solve an optimal stopping problem for X with partial observation, i.e. where the moment of stopping is required to be a stopping time with respect to the natural filtration of Y
Backward stochastic differential equations and optimal control of marked point processes
Full text linkWe study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution on the data. We next address optimal control problems for point processes of general non-Markovian type and show that BSDEs can be used to prove existence of an optimal control and to represent the value function. Finally we introduce a Hamilton--Jacobi--Bellman equation, also stochastic and of backward type, for this class of control problems: when the state space is finite or countable we show that it admits a unique solution which identifies the (random) value function and can be represented by means of the BSDEs introduced above
Backward stochastic differential equations associated to jump Markov processes and applications
Full text linkIn this paper we study backward stochastic differential equations (BSDEs) driven by the compensated
random measure associated to a given pure jump Markov process X on a general state space K. We apply
these results to prove well-posedness of a class of nonlinear parabolic differential equations on K, that
generalize the Kolmogorov equation of X. Finally we formulate and solve optimal control problems for
Markov jump processes, relating the value function and the optimal control law to an appropriate BSDE
that also allows to construct probabilistically the unique solution to the Hamilton–Jacobi–Bellman equation
and to identify it with the value function
Linear-quadratic optimal control under non-Markovian switching
Full text linkWe study an infinite-dimensional continuous-time optimal control problem on finite horizon for a
controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic
coecients, possibly depending on an underlying independent marked point process, so that our
model is general enough to include controlled switching systems where the switching mechanism is not
required to be Markovian. The problem is solved by means of a Riccati equation, which a backward
stochastic differential equation driven by the Bronwian motion and by the random measure associated
to the marked point process
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