arXiv subjects

Sarvesh Ravichandran Iyer

Publications and source records attributed to Sarvesh Ravichandran Iyer.

4 recordsLinked to original sources

arXiv2026

Generating DDPM-based Samples from Tilted Distributions

Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $θ\in \mathbb{R}^d$. We define a plug-in estimator and show that it is minimax-optimal. We develop Wasserstein bounds between the distribution of the plug-in estimator and the true distribution as a function of $n$ and $θ$, illustrating regimes where the output and the desired true distribution are close. Further, under some assumptions, we prove the TV-accuracy of running Diffusion on these tilted samples. Our theoretical results are supported by extensive simulations. Applications of our work include finance, weather and climate modelling, and many other domains, where the aim may be to generate samples from a tilted distribution that satisfies practically motivated moment constraints.

cs.LG↗

arXiv2026

Fast random sampling and small noise analysis for stochastic control models

In this paper, we study a linear control system with a given state feedback law. The system is influenced by rapid random sampling occurring at frequency $\frac 1n, n \in \mathbb N$, as well as by white noise of small intensity $\varepsilon \in (0, 1]$. We study the behavior of the system as $n \to \infty$ and $\varepsilon \searrow 0$ jointly, and prove that it converges to its ideal deterministic analogue. For the random fluctuations around its analogous deterministic trajectory, we obtain either stochastic differential equations or an ordinary differential equation depending on the joint behavior of $\varepsilon$ and $n$. Further, we extend this problem to a nonlinear system driven by multiplicative white noise, where the noise intensity is scaled by a small parameter. In this case, we again perform a similar analysis as in the linear case.

math.PR↗

arXiv2025

Fundamental limits for weighted empirical approximations of tilted distributions

Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in rare event simulation. In this article, we discuss the asymptotic efficiency of a self-normalized importance sampler of the tilted distribution. We provide a sharp characterization of its accuracy, given the number of samples and the degree of tilt. Our findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions.

math.ST↗

arXiv2024

The martingale problem for geometric stable-like processes

We prove that the martingale problem is well posed for pure-jump Lévy-type operators of the form $$ (\mathcal Lf)(x) = \int_{\mathbb R^d \setminus \{0\}} \left(f(x+h)-f(x) - (\nabla f(x) \cdot h)1_{\|h\| < 1}\right)K(x,h) dh, $$ where $K(x,\cdot)$ is a jump kernel of the form $K(x,h) \sim \frac{l(\|h\|)}{\|h\|^d}$ for each $x \in \mathbb R^d,\|h\|<1$, and $l$ is a positive function that is slowly varying at $0$, under suitable assumptions on $K$. This includes jump kernels such as those of $α$-geometric stable processes, $α\in (0,2]$.

math.PR↗