The longer you hold a quality stock, the less it matters what initial price you paid. That's not to say valuation doesn't matter, but prolonged growth goes a long way to mitigating any premium you might have paid. For investors looking for artificial intelligence (AI) stocks they can trust with their hard-earned money, getting the choices right should come above all else.

If AI is genuinely a multitrillion-dollar economic opportunity, as researchers believe, Snowflake (SNOW -0.44%), Arm Holdings (ARM 1.26%), and Palantir Technologies (PLTR 1.38%) could crush the market for years and decades to come and their prices now don't matter as much.

Here is a closer look at all three stocks. Be warned: None of these stocks have cheap valuations today. However, buying slowly over time and strong performance from the underlying businesses can take care of your portfolio. The best part is that you can buy multiple shares of all three for less than $1,000.

1. Snowflake

Investors have gone a bit crazy lately for semiconductor stocks. Yes, the chips power the data centers that run AI, but the artificial intelligence technology is only as good as the data it's trained on. Just think of all the data a company might have: customer data, internal operations data, and financial data -- on countless spreadsheets. That's where Snowflake comes in.

The company's platform stores data in the cloud, which can be easily searched, shared, and integrated with various third-party apps. It works across all major public clouds like Microsoft Azure, Amazon Web Services (AWS), and Alphabet's Google Cloud and charges based on usage, so it's always priced according to what customers need. More data and more customers over time mean more growth for Snowflake.

SNOW Revenue (TTM) Chart

SNOW Revenue (TTM) data by YCharts; TTM = trailing 12 months.

Snowflake could become a central hub for thousands of companies to use and exchange data in an industry where AI is at the top of their minds. The company recently got a new CEO, Sridhar Ramaswamy, who previously headed Snowflake's AI unit.

That should tell you where the company's strategic focus is. The future looks bright for the company and its shareholders.

2. Arm Holdings

Manufacturing chips starts with design and getting the fundamentals of the various designs right, and Arm Holdings is a titan in chip design. The company earns licensing fees and royalties on its designs and intellectual property.

Arm management estimates that nearly half the world's chips use Arm designs. That makes Arm an asset-light and profitable company bound to grow as an increasingly technology-driven world uses more and more chips.

How many more? Arm was founded in 1990, and since then, more than 280 billion chips have been built based on its intellectual property. That includes over 30 billion chips in Arm's most recent fiscal year -- over 10% of its chips in the past year alone. In other words, chip demand is increasing exponentially and could drive substantial growth for years.

ARM Revenue (TTM) Chart

ARM revenue (TTM) data by YCharts.

The company is already converting 26% of its revenue into free cash flow, and it has $2.4 billion in cash on hand and zero debt. I expect eventual share repurchases to boost earnings growth. The company looks like a future share cannibal, devouring its stock (through buybacks) to increase investment returns.

Arm is a fixture in the chip world, making the stock one you can hold indefinitely. The valuation is very rich today, so investors might want to wait for a pullback before buying too aggressively.

3. Palantir Technologies

There are so many software companies on Wall Street that finding the exceptional ones can be challenging. But Palantir Technologies seems to fit the bill.

The company operates platforms for building and deploying custom software applications for businesses and government. It has traditionally done so with its Gotham and Foundry platforms, but its new Artificial Intelligence Platform (AIP) is geared toward AI applications.

Revenue growth has accelerated since launching AIP midway through last year, and CEO Alex Karp said in the most recent shareholder letter that it represents the company's future.

Financially, Palantir is gushing cash flow, converting 31% of revenue into free cash. The business also possesses a war chest of $3.6 billion against zero debt.

PLTR Revenue (TTM) Chart

PLTR revenue (TTM) data by YCharts.

And it could just be getting started. The company has only 497 customers, while tens of thousands of corporations in the U.S. and worldwide could need AI to compete in the future.

Palantir stock was a bit more speculative when it first went public because of the secretive nature of its ties to the government, from which it gets roughly half its revenue. But its commercial momentum could give investors confidence that its success will translate nicely to the private sector over the coming years.

Want to invest? Here is your playbook

These three stocks offer exciting long-term potential but also come with lofty valuations. Each has an elevated forward price-to-earnings ratio, ranging from 70 to 170 times earnings. Even though profits will likely grow fast for all three companies, it's still a tremendous premium to the broader market. The S&P 500 trades at just 21 times earnings.

SNOW PE Ratio (Forward) Chart

SNOW PE Ratio (Forward) data by YCharts

If you want to buy, consider dollar-cost averaging into the position slowly to have some money left if the market offers them up at lower prices. Buy slowly, hold for a long time, and investors should be pleased with the results.