Related papers: A stochastic fixed point equation for weighted min…

We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…

This article study the fractional Hamiltonian systems \begin{eqnarray}\label{00} {_{t}}D_{\infty}^{\alpha}({_{-\infty}}D_{t}^{\alpha}u) + \lambda L(t)u = \nabla W(t, u), \;\;t\in \mathbb{R}, \end{eqnarray} where $\alpha \in (1/2, 1)$,…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

In this paper we consider the general fractional equation \sum_{j=1}^m \lambda_j \frac{\partial^{\nu_j}}{\partial t^{\nu_j}} w(x_1,..., x_n ; t) = -c^2 (-\Delta)^\beta w(x_1,..., x_n ; t), for \nu_j \in (0,1], \beta \in (0,1] with initial…

This paper is devoted to the weighted estimates and the solvability of time-fractional parabolic equations. The leading coefficients \(a^{ij}(t,x)\) are assumed to have small mean oscillations in \((t,x)\) locally, in both non-divergence…

One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our…

Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…

In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify these as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general…

Given $d \ge 1$, let $(A_i)_{i\ge 1}$ be a sequence of random $d\times d$ real matrices and $Q$ be a random vector in $\mathbb{R}^d$. We consider fixed points of multivariate smoothing transforms, i.e. random variables $X\in \mathbb{R}^d$…

We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…

Let $N,d > 1$ be fixed integers, let $(T_1, ..., T_N)$ be random d-by-d matrices with nonnegative entries and $Q$ a random d-vector with nonnegative entries. This induces a mapping (the multivariate smoothing transform) on probability laws…

This paper combines the decomposition technique ($\sigma$-stability) in random functional analysis with the deterministic theory of asymptotically pointwise contractions to provide a complete self-contained derivation of a fixed point…

For two collections of nonnegative and suitably normalised weights $\W=(\W_j)$ and $\V=(\V_{n,k})$, a probability distribution on the set of partitions of the set $\{1,...,n\}$ is defined by assigning to a generic partition $\{A_j, j\leq…

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

We described a method to solve deterministic and stochastic Walras equilibrium models based on associating with the given problem a bifunction whose maxinf-points turn out to be equilibrium points. The numerical procedure relies on an…

We consider the following stochastic partial differential equation on $t \geq 0, x\in[0,J], J \geq 1$ where we consider $[0,J]$ to be the circle with end points identified: \begin{equation*} \partial_t{\mathbf u}(t,x)…

We consider a fixed-point equation for a non-negative integer-valued random variable, that appears in branching processes with state-independent immigration. A similar equation appears in the analysis of a single-server queue with a…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…