1.

Record Nr.

UNINA9910299967303321

Autore

Friz Peter K

Titolo

A Course on Rough Paths : With an Introduction to Regularity Structures / / by Peter K. Friz, Martin Hairer

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014

ISBN

3-319-08332-5

Edizione

[1st ed. 2014.]

Descrizione fisica

1 online resource (XIV, 251 p. 2 illus.)

Collana

Universitext, , 0172-5939

Disciplina

519.2

Soggetti

Probabilities

Differential equations

Differential equations, Partial

Probability Theory and Stochastic Processes

Ordinary Differential Equations

Partial Differential Equations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

Introduction -- The space of rough paths -- Brownian motion as a rough path -- Integration against rough paths -- Stochastic integration and Itˆo’s formula -- Doob–Meyer type decomposition for rough paths -- Operations on controlled rough paths -- Solutions to rough differential equations -- Stochastic differential equations -- Gaussian rough paths -- Cameron–Martin regularity and applications -- Stochastic partial differential equations -- Introduction to regularity structures -- Operations on modelled distributions -- Application to the KPZ equation.

Sommario/riassunto

Lyons’ rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic



arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension – the theory of regularity structures – and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background.

2.

Record Nr.

UNINA9910484872903321

Titolo

DNA Computing and Molecular Programming : 23rd International Conference, DNA 23, Austin, TX, USA, September 24–28, 2017, Proceedings / / edited by Robert Brijder, Lulu Qian

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017

ISBN

3-319-66799-8

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (XII, 267 p. 76 illus.)

Collana

Theoretical Computer Science and General Issues, , 2512-2029 ; ; 10467

Disciplina

006.3842

Soggetti

Computer science

Algorithms

Bioinformatics

Artificial intelligence

Artificial intelligence - Data processing

Computer science - Mathematics

Discrete mathematics

Theory of Computation

Computational and Systems Biology

Artificial Intelligence

Data Science

Discrete Mathematics in Computer Science

Lingua di pubblicazione

Inglese



Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Algorithms and models for computation with biomolecular systems -- Computational processes in vitro  and in vivo -- Molecular motors and molecular robotics -- Studies of fault-tolerance and error correction -- Software tools for analysis, simulation, and design -- Synthetic biology and in vitro evolution -- Applications in engineering, physics, chemistry,  biology, and medicine.

Sommario/riassunto

This book constitutes the refereed proceedings of the 23th International Conference on DNA Computing and Molecular Programming, DNA 23, held Austin, TX, USA, in September 2017. The 16 full papers presented were carefully selected from 23 submissions. Research in DNA computing aims to draw together mathematics, computerscience, physics, chemistry, biology, and nanotechnology to address the analysis, design, and synthesis of information-based molecular systems. The papers address all areas related to biomolecular computing such as: algorithms and models for computation with biomolecular systems; computational processes in vitro and in vivo; molecular motors and molecular robotics; studies of fault-tolerance and error correction; software tools for analysis, simulation, and design; synthetic biology and in vitro evolution; applications in engineering, physics, chemistry, biology, and medicine.  .