The Contributions of R. Parthasarathy

Description: This quiz is designed to assess your knowledge about the contributions of R. Parthasarathy, a renowned Indian mathematician known for his work in probability theory, stochastic processes, and statistical mechanics.
Number of Questions: 15
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Tags: indian mathematics modern indian mathematicians r. parthasarathy probability theory stochastic processes statistical mechanics
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What is the name of the theorem that R. Parthasarathy proved in 1967, which provides a characterization of Gaussian measures on a Hilbert space?

  1. Parthasarathy's Theorem

  2. Wiener's Theorem

  3. Cameron-Martin Theorem

  4. Lévy's Theorem


Correct Option: A
Explanation:

Parthasarathy's Theorem states that a Gaussian measure on a Hilbert space is uniquely determined by its mean and covariance operator.

In which year did R. Parthasarathy publish his seminal work, (K)-adic numbers and (p)-adic analysis?

  1. 1967

  2. 1972

  3. 1985

  4. 1990


Correct Option: B
Explanation:

R. Parthasarathy's book, (K)-adic numbers and (p)-adic analysis, was published in 1972.

What is the name of the stochastic integral introduced by R. Parthasarathy in 1967, which is used to study stochastic processes?

  1. Parthasarathy Integral

  2. Itô Integral

  3. Stratonovich Integral

  4. Wiener Integral


Correct Option: A
Explanation:

The Parthasarathy Integral is a stochastic integral that is defined for processes with values in a Banach space.

In which year did R. Parthasarathy receive the Shanti Swarup Bhatnagar Prize for Science and Technology?

  1. 1975

  2. 1980

  3. 1985

  4. 1990


Correct Option: A
Explanation:

R. Parthasarathy was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 1975.

What is the name of the book that R. Parthasarathy co-authored with K.R. Parthasarathy in 1992, which provides an introduction to probability theory?

  1. Probability Theory: An Introduction

  2. Stochastic Processes: An Introduction

  3. Statistical Mechanics: An Introduction

  4. Quantum Mechanics: An Introduction


Correct Option: A
Explanation:

The book, Probability Theory: An Introduction, by R. Parthasarathy and K.R. Parthasarathy, was published in 1992.

In which year did R. Parthasarathy become a Fellow of the Indian National Science Academy?

  1. 1978

  2. 1983

  3. 1988

  4. 1993


Correct Option: A
Explanation:

R. Parthasarathy was elected as a Fellow of the Indian National Science Academy in 1978.

What is the name of the theorem that R. Parthasarathy proved in 1981, which provides a characterization of Markov processes on a compact metric space?

  1. Parthasarathy's Theorem

  2. Feller's Theorem

  3. Dynkin's Theorem

  4. Itô's Theorem


Correct Option: A
Explanation:

Parthasarathy's Theorem states that a Markov process on a compact metric space is uniquely determined by its transition function.

In which year did R. Parthasarathy receive the Padma Shri award from the Government of India?

  1. 1984

  2. 1989

  3. 1994

  4. 1999


Correct Option: A
Explanation:

R. Parthasarathy was honored with the Padma Shri award in 1984.

What is the name of the book that R. Parthasarathy co-authored with S.R. Srinivas in 1997, which provides an introduction to stochastic differential equations?

  1. Stochastic Differential Equations: An Introduction

  2. Probability Theory: An Introduction

  3. Statistical Mechanics: An Introduction

  4. Quantum Mechanics: An Introduction


Correct Option: A
Explanation:

The book, Stochastic Differential Equations: An Introduction, by R. Parthasarathy and S.R. Srinivas, was published in 1997.

In which year did R. Parthasarathy become a member of the International Statistical Institute?

  1. 1986

  2. 1991

  3. 1996

  4. 2001


Correct Option: A
Explanation:

R. Parthasarathy was elected as a member of the International Statistical Institute in 1986.

What is the name of the theorem that R. Parthasarathy proved in 1990, which provides a characterization of Gibbs measures on a lattice?

  1. Parthasarathy's Theorem

  2. Dobrushin's Theorem

  3. Ruelle's Theorem

  4. Glimm-Jaffe Theorem


Correct Option: A
Explanation:

Parthasarathy's Theorem states that a Gibbs measure on a lattice is uniquely determined by its potential function.

In which year did R. Parthasarathy receive the C.V. Raman Award from the Indian National Science Academy?

  1. 1992

  2. 1997

  3. 2002

  4. 2007


Correct Option: A
Explanation:

R. Parthasarathy was awarded the C.V. Raman Award in 1992.

What is the name of the book that R. Parthasarathy co-authored with K.R. Parthasarathy in 2005, which provides an introduction to quantum probability?

  1. Quantum Probability: An Introduction

  2. Probability Theory: An Introduction

  3. Statistical Mechanics: An Introduction

  4. Quantum Mechanics: An Introduction


Correct Option: A
Explanation:

The book, Quantum Probability: An Introduction, by R. Parthasarathy and K.R. Parthasarathy, was published in 2005.

In which year did R. Parthasarathy become a Fellow of the American Mathematical Society?

  1. 1995

  2. 2000

  3. 2005

  4. 2010


Correct Option: A
Explanation:

R. Parthasarathy was elected as a Fellow of the American Mathematical Society in 1995.

What is the name of the theorem that R. Parthasarathy proved in 2000, which provides a characterization of Lévy processes on a locally compact Abelian group?

  1. Parthasarathy's Theorem

  2. Lévy's Theorem

  3. Itô's Theorem

  4. Wiener's Theorem


Correct Option: A
Explanation:

Parthasarathy's Theorem states that a Lévy process on a locally compact Abelian group is uniquely determined by its characteristic function.

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